PRP Records

Probable Primes Top 10000

(173006 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


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1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 30000) Who ? When ?
90012^168823+102550821Lelio R Paula01/2009
90027*10^50818-8950819Robert Price01/2017
90042^168811+15015*16881150818Henri Lifchitz02/2005
90032^168813-283350818Yves Minet09/2014
9005(12413^12413+3221)/2/8950816Makoto Morimoto07/2016
90062^168795+538550813Lelio R Paula05/2009
90074*3^106483+550806Lelio R Paula03/2014
900813^45606+450803Lelio R Paula01/2013
900913^45606-3850803Lelio R Paula01/2013
90102^168746+5890550798Lelio R Paula05/2009
9011(16*10^50795-43)/950796Robert Price02/2015
9012gcd(V(615445),5*F(123089)*(F(123089)-1)+1)50794Serge Batalov04/2015
90137*10^50789-4750790Robert Price02/2017
90142^168717-72952350789Paul Bourdelais11/2012
9015(12409^12409+136)/5^2/13/5647/47327950788Makoto Morimoto07/2016
9016(21*2^168652-1)/21550769Lelio R Paula01/2014
90172^168629+1290950763Lelio R Paula01/2011
90189328^12787+12787^932850762Norbert Schneider01/2016
90192^168627+7311350762Enzo Doria04/2016
90202^168623+4733350761Yves Minet02/2010
9021(12401^12401+154)/3^2/5/31/59/67/97/761/863/1214350745Makoto Morimoto07/2016
9022(lucasV(1,2,337126)+2)/(5*11)50739Mike Oakes02/2017
9023(17^41221+1)/1850720Paul Bourdelais03/2010
902410^50711+750712Jason Earls12/2007
902510^50711-31796950711Patrick De Geest04/2009
9026(17^41213+3^41213)/2050710Robert Price08/2013
9027(12391^12391+58)/59/211/782350710Makoto Morimoto07/2016
90292^168431-15950703Lelio R Paula01/2011
9028(7*10^50702-1)/350703Erik Branger03/2014
9030117216#-p(117216)50700Henri Lifchitz03/2007
9031(1543550^8192+1)/6553750692Syoichiro Yamada06/2008
9032(13*2^168352-1)/47750678Lelio R Paula01/2014
90338*10^50675+3950676Robert Price01/2017
9034(lucasV(1,2,336840)+2)/(113*337*23609*70589*125621*144481)50676Mike Oakes02/2017
903514415^3274+3274^1441550670Hans Havermann05/2016
9036(12379^12379+282)/1750663Makoto Morimoto07/2016
90385^72480-1712650662Enzo Doria02/2013
9037(34*10^50667-7)/9/3^3/13627750662Makoto Morimoto04/2016
90393^106143+250644Mike Oakes11/2009
90409178^12777-12777^917850633Norbert Schneider02/2017
9041(2*10^50603-41)/350603Robert Price01/2017
9042(12^46889-1)/1150601Paul Bourdelais09/2008
90432^168068-189350594Yves Minet09/2012
90442^168057+841550591Lelio R Paula11/2011
90454*10^50579+950580Robert Price05/2015
90462^168019-9439550579Lelio R Paula07/2011
90472^168019+7421350579Enzo Doria04/2016
90483^106002+7050576Lelio R Paula07/2012
90495*2^167970-950565Lelio R Paula02/2014
9050(58*10^50558-13)/950559Robert Price09/2015
905188*10^50547+750549Robert Price11/2016
90522^167910-11262550546Enzo Doria06/2014
9053(1476500^8192+1)/6553750534Syoichiro Yamada06/2008
90542^167866+1171550533Lelio R Paula05/2009
9055gcd(V(621415),5*F(124283)*(F(124283)+1)+1)50528Serge Batalov04/2015
90562^167847-13550527Lelio R Paula01/2011
9057-lucasV(-1,2,335684)50526Mike Oakes01/2017
9058(-lucasV(1,2,335677)+2)/(3*226777)50519Mike Oakes02/2017
9059(12347^12347+1567)/2/3^2/550517Makoto Morimoto07/2016
90612^167807+7550515Lelio R Paula08/2010
90602^167805+7627750515Enzo Doria04/2016
90628335^12882+12882^833550510Norbert Schneider03/2016
90637*2^167777+950507Lelio R Paula02/2014
906414162^3681+3681^1416250502Hans Havermann05/2016
9065(17*10^50495-11)/350496Robert Price07/2015
90662^167682+8550478Lelio R Paula08/2010
90672^167667-92742750473Paul Bourdelais11/2012
90689737^12654+12654^973750470Norbert Schneider01/2016
9069(9179*2^167644-1)/1750469Lelio R Paula03/2015
907013386^5891+5891^1338650468Hans Havermann05/2016
9071(lucasV(1,2,335347)+2)/(3*5*11*302287*439661)50462Mike Oakes02/2017
90725003^13637-15650447Enzo Doria07/2012
90736^64826-2672350445Enzo Doria03/2013
9074(3^105718+7)/3250439Lelio R Paula03/2012
9075(1436724^8192+1)/6553750437Syoichiro Yamada06/2008
907617^40989+5650435Lelio R Paula01/2013
9077(12329^12329+1652)/42150435Makoto Morimoto07/2016
90782*5^72153+750434Lelio R Paula09/2014
9079(3126^14431-1)/312550433Richard Fischer03/2015
908039^31694+3850428Norbert Schneider05/2014
90812^167460+218750411Lelio R Paula11/2011
9082(12323^12323+2709)/2^450409Makoto Morimoto07/2016
908311^48400-771050404Enzo Doria02/2013
90842^167432+5461550403Lelio R Paula05/2009
9085(23*2^167430-1)/416950400Lelio R Paula01/2014
908619^39404+2250389Lelio R Paula01/2013
908735^32629-783450382Enzo Doria03/2013
90896^64744+16350381Lelio R Paula06/2012
9088116447#+17465950381Nicolas PALAU09/2016
90912^167353+12950379Lelio R Paula05/2009
909020^38722-113350379Enzo Doria03/2013
90923^105567-1650369Lelio R Paula07/2012
90932^167321-11284950369Enzo Doria06/2014
9094(28*10^50362-43)/350363Robert Price04/2016
909511421^12410-12410^1142150357Norbert Schneider08/2013
90962^167278-206350356Yves Minet03/2013
9097181^22300+22300^18150347Serge Batalov05/2014
90989932^12595-12595^993250343Norbert Schneider12/2016
90998993^12732-12732^899350342Norbert Schneider02/2017
91003*5^72018-450339Lelio R Paula09/2014
91012^167207-11268750335Enzo Doria06/2014
91026^64674-3750327Lelio R Paula06/2012
91032^167177+7480150326Enzo Doria04/2016
910413739^4600+4600^1373950323Hans Havermann10/2015
910511508^12391+12391^1150850320Norbert Schneider06/2014
91062^167132-216350312Yves Minet08/2013
91077^59527-6250307Lelio R Paula06/2012
9109(310027^9161+1)/31002850302Faysal YAtim04/2008
9108(12301^12301+74)/3^2/5^3/11/17/115150302Makoto Morimoto07/2016
91102^167083-11251950297Enzo Doria06/2014
9111272^20659-20659^27250296Norbert Schneider09/2015
911225337!!-1650290Robert Price06/2015
91139722^12611-12611^972250290Norbert Schneider12/2016
9115(15*2^167013+1)/64950275Lelio R Paula07/2012
911419^39315-1250275Lelio R Paula01/2013
91165^71925-3650274Lelio R Paula06/2012
91172^167002+279913950273Enzo Doria04/2016
911810957^12444-12444^1095750270Norbert Schneider07/2013
91198*10^50253-9950254Robert Price02/2017
91215^71894-5450252Lelio R Paula06/2012
9120(127^23887+1)/12850252Richard Fischer04/2017
912218^40028-550247Lelio R Paula01/2013
9123(3*2^166904+1)/127950241Lelio R Paula07/2012
912424^36397+2350236Norbert Schneider12/2013
91257984*29^34345+2150230Curtis Bright05/2015
91263^105248-1352850217Enzo Doria02/2013
91276^64532-6550216Lelio R Paula06/2012
91285^71834-2061650210Enzo Doria03/2013
9129(31*2^166778-1)/365150204Lelio R Paula01/2014
91302^166752-11239750198Enzo Doria06/2014
9131(12277^12277+1746)/17/37/15150197Makoto Morimoto07/2016
913211^48199-93050195Enzo Doria11/2012
91333*10^50194-750195Erik Branger11/2013
91349992^12549+12549^999250192Norbert Schneider10/2015
91352^166708+15750185Lelio R Paula01/2011
9136(1338272^8192+1)/6553750184Syoichiro Yamada06/2008
91377*2^166685+350179Lelio R Paula02/2014
91387*2^166671-950174Lelio R Paula02/2014
91399*2^166670+750174Lelio R Paula02/2014
91402^166670-11254150173Enzo Doria06/2014
91412^166657+46550169Lelio R Paula11/2011
914217^40768-2050163Lelio R Paula01/2013
91432^166596-7879550151Lelio R Paula07/2011
9144135^23541+13450151Norbert Schneider04/2015
914624^36335-67350150Enzo Doria03/2013
9145(12269^12269+291)/2^8/5/7/19/41/109/1042634950150Makoto Morimoto07/2016
9147(28*10^50147-97)/350148Robert Price07/2016
9148263^20718-20718^26350137Norbert Schneider09/2015
9149t(167020)50133Robert Price01/2015
9150(12263^12263+1442)/127/547950133Makoto Morimoto07/2016
91512868*(2340*(29023#-29527)*(2340*(29023#-29527)+3)+1)*(2868*(2340*(29023#-29527)*(2340*(29023#-29527)50129Pierre CAMI06/2008
915212^46445-1950123Lelio R Paula12/2012
91532^166501-1459350122Enzo Doria04/2013
9154(31*2^166509-1)/368407750120Lelio R Paula01/2014
91552^166483-16950117Lelio R Paula01/2011
91569^52515+2*6^52515-4^5251550113Mike Oakes04/2010
9157(23*2^166487-1)/3377049950112Lelio R Paula01/2014
91582*5^71689-950109Lelio R Paula09/2014
915913495^5154+5154^1349550096Hans Havermann04/2016
91606^64369-11950089Lelio R Paula06/2012
91619224^12633-12633^922450089Norbert Schneider12/2016
91622^166370-11254150083Enzo Doria06/2014
9163(12253^12253+1454)/3^3/251/947/29242750081Makoto Morimoto07/2016
91642^166339-11232150074Enzo Doria06/2014
91655^71637-2250073Lelio R Paula06/2012
9166Phi(50131,10)/89010999409/9123691040118653/18020045580157867/3062191531806380194750068Maksym Voznyy01/2013
91675^71618-1382650059Enzo Doria02/2013
916815^42563-250058Lelio R Paula11/2012
91691943^15222+15222^194350058Serge Batalov05/2014
917011641^12310+12310^1164150053Norbert Schneider04/2014
917113537!-2^13537+150052Joe McLean06/2006
91722^166227-16446750040Gary Barnes08/2009
917312241^12241+475650039Makoto Morimoto07/2016
9174(106*10^50035-1)/350037Serge Batalov12/2014
917511^48044-81050033Enzo Doria11/2012
917615^42539+8850030Lelio R Paula11/2012
9177524^18397-523^1839750028Jean-Louis Charton10/2009
91782^166159-1449750019Enzo Doria04/2013
91792^166155+8785550018Lelio R Paula01/2009
91802^166138-1165550013Lelio R Paula07/2011
91852^166104-11262550003Enzo Doria06/2014
9181(L(239265)-1)/5-2^90650003Jorge Menendez03/2017
9182(L(239265)-1)/5-2^315250003Jorge Menendez04/2017
9183(L(239265)-1)/5-2^2015550003Jorge Menendez04/2017
9184(L(239265)-1)/5-2^7891250003Jorge Menendez04/2017
91862^166100+19901550002Lelio R Paula05/2008
918810^50000+6585950001Milton L. Brown02/2006
9187(598*10^49999-31)/950001Robert Price02/2017
918910^49999+9170150000Patrick De Geest03/2005
920910^50000-19430350000Patrick De Geest02/2009
9190(2^74207281/10^948782)%10^5000050000Michael Vang04/2016
9191(2^57885161/10^11608093)%10^5000050000Michael Vang05/2016
9192(2^43112609/10^788658)%10^5000050000Michael Vang05/2016
9193(2^42643801/10^3670320)%10^5000050000Michael Vang05/2016
9194(2^37156667/10^412682)%10^5000050000Michael Vang05/2016
9195(2^32582657/10^7836670)%10^5000050000Michael Vang05/2016
9196(2^24036583/10^3069021)%10^5000050000Michael Vang05/2016
9197(2^25964951/10^5214128)%10^5000050000Michael Vang05/2016
9198(2^13466917/10^157937)%10^5000050000Michael Vang05/2016
9199(2^20996011/10^6193479)%10^5000050000Michael Vang05/2016
9200(2^6972593/10^381525)%10^5000050000Michael Vang05/2016
9201(2^30402457/10^1629036)%10^5000050000Michael Vang05/2016
9202(2^3021377/10^702316)%10^5000050000Michael Vang05/2016
9203(2^1398269/10^37827)%10^5000050000Michael Vang05/2016
9204(2^2976221/10^767789)%10^5000050000Michael Vang05/2016
9205(2^859433/10^42285)%10^5000050000Michael Vang06/2016
9206(2^1257787/10^119173)%10^5000050000Michael Vang06/2016
9207(2^756839/10^136257)%10^5000050000Michael Vang06/2016
92082*10^49999+36350000Makoto Morimoto09/2016
921010^49999-414949999Patrick De Geest02/2009
921110484^12433-12433^1048449988Norbert Schneider07/2013
92122^166052+14549987Lelio R Paula01/2011
9213(10^50001+10936)/(2^3*19*241*5872003*15974507)49983Makoto Morimoto09/2016
92141111*2^166022-55549981Henri Lifchitz02/2005
921511^47993+3049980Lelio R Paula10/2012
92162^166000-7879549971Lelio R Paula07/2011
921713517!-13517#+14997003/2005
92182^165995-11322749970Enzo Doria07/2014
9219(12227^12227+1092)/5/11/17/37^249970Makoto Morimoto07/2016
922017^40609+1449968Lelio R Paula11/2012
9222(1257656^8192+1)/6553749963Syoichiro Yamada06/2008
9221(3^104735-8)/149319993149963Lelio R Paula03/2012
92232^165969-11271149962Enzo Doria06/2014
92242^165910-760549944Lelio R Paula04/2009
922536313!3-5904949942Robert Price12/2015
92262^165884-4549937Lelio R Paula08/2010
9227(1246892^8192+1)/6553749933Syoichiro Yamada06/2008
92283^104654+10449933Lelio R Paula07/2012
92299035^12622+12622^903549932Norbert Schneider01/2016
9230(22699*2^165838+1)/328749924Lelio R Paula05/2014
92316^64149-8549918Lelio R Paula06/2012
9232(7*10^49913+71)/349914Robert Price03/2016
92332^165799-11481749911Enzo Doria05/2015
92342^165789+3549908Lelio R Paula08/2010
92352^165783-12149906Lelio R Paula01/2011
92362^165760-11264949899Enzo Doria06/2014
9237(11*2^165758+1)/13549898Lelio R Paula01/2012
92382^165747+6349895Lelio R Paula04/2009
9239(7*10^49893-13)/349894Robert Price06/2016
9240298^20163-20163^29849888Norbert Schneider08/2015
9241(49885^49885)/(10^184474)49885James G. Merickel08/2015
924217^40540+3649883Lelio R Paula11/2012
9243(12211^12211+4312)/13/17/31/1297/1483/1627/9923/3643349882Makoto Morimoto07/2016
92442^165676-11294949874Enzo Doria06/2014
9245(12203^12203+992)/1149867Makoto Morimoto07/2016
92467784^12811-12811^778449851Norbert Schneider03/2017
92472^165581-74549845Yves Minet01/2012
92482^165576+7482149844Enzo Doria04/2016
924913318^5527+5527^1331849843Hans Havermann04/2016
9250(12197^12197+1755)/2^449839Makoto Morimoto07/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 25 2017 10:58 (Time in France)

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